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Homework Statement
A linear harmonic oscillator is subject to friction(stokes). The Oscillator gets an Impulse at the time t = 0 at the rest position. What is the equation of motion for the time interval 0 - t0?
Homework Equations
Friction force: Fr = -a * x'(t); a = constant (stokes friction)
Impulse: F(t) = m *v0 / t0 (for 0 <= t <= t0)
k = spring constant
m = mass
x(t = 0) = 0 (rest position at the time t = 0)
x'(t = 0) = 0 (velocity at the time t = 0 is zero)
The Attempt at a Solution
I have a little trouble with the impulse here. My attempt at a solution was this:
m*x'' = -k*x - a*x' + m*v0/t0 ==> x'' + (a/m)*x' + (k/m)*x = v0 / t0
But my book claims that the equation really goes like this:
x'' + (a/m)*x' + (k/m)*x = v0 / t0 * (1/m)
Does somebody know why I am wrong and the book is right? I don't understand it, because I thought I needed a force(respectively acceleration) in above equation of motion. How does v0 / t0 * (1/m) fit into the equation, doesn't it have the wrong units?
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